Question 935990
this was a doozy, but i think i was able to figure it out.


by the log conversion formula, you get:


{{{log(3,7) = log(7)/log(3)}}} and {{{log(4,3) = log(3)/log(4)}}} and {{{log(6,7) = log(6)/log(7)}}}


you get the following equation:


({{{ log( 3, 7 ) * log( 4, 3 ) * log( 7, 6 ) }}}) = {{{log(7)/log(3) * log(3)/log(4) * log(6)/log(7)}}}


{{{log(7)}}} in the numerator and denominator cancel out, and {{{log(3)}}} in the numerator and denominator cancel out and you are left with {{{log(6) / log(4)}}}



by the log base conversion formula, you get:


{{{log(4,6) = log(6) / log(4)}}} and so your final solution is:


({{{ log( 3, 7 ) * log( 4, 3 ) * log( 7, 6 ) }}} = {{{ log(4,6)}}}.


to confirm the solution is correct, you have to go back to the log conversion formulas.


{{{ log(4,6)}}}.= {{{log(6)/log(4)}}} = 1.29248125.


({{{ log( 3, 7 ) * log( 4, 3 ) * log( 7, 6 ) }}}) = {{{log(7)/log(3) * log(3)/log(4) * log(6)/log(7)}}} = 1.29248125.


they give you the same value, so they're equivalent.


your solution is that the expression becomes {{{log(4,6)}}}